Lia has 72 green grapes that are shared equally between 8 of her friends. Darrel adds 41 green grapes to his share. How many grapes does Darrel have in all

Using the normal distribution, it is found that:

a) The 65th percentile is of 37.31.

b) The 90th percentile is of 42.68.

c) There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.

d) There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Question a:

The 65th percentile is X when Z has a p-value of 0.65, so X when Z = 0.385.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.385 = \frac{X - 35}{6}[/tex]

[tex]X - 35 = 0.385(6)[/tex]

[tex]X = 37.31[/tex]

The 65th percentile is of 37.31.

Question b:

The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 35}{6}[/tex]

[tex]X - 35 = 1.28(6)[/tex]

[tex]X = 42.68[/tex]

The 90th percentile is of 42.68.

Question c:

The probability is the p-value of Z when X = 38 subtracted by the p-value of Z when X = 28, hence:

X = 38:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{38 - 35}{6}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

X = 28:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{28 - 35}{6}[/tex]

[tex]Z = -1.17[/tex]

[tex]Z = -1.17[/tex] has a p-value of 0.121.

0.6915 - 0.121 = 0.5705.

There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.

Question d:

The probability is the p-value of Z when X = 44 subtracted by the p-value of Z when X = 41, hence:

X = 44:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{44 - 35}{6}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a p-value of 0.9332.

X = 41:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{41 - 35}{6}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.8413.

0.9332 - 0.8413 = 0.0919

There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.

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Answer:

x= 5/3

Step-by-step explanation:

You would set the equations equal to each other, so 2x + 3 = -x + 8. Then, you would add the x to the 2x making it 3x. That makes your equation 3x + 3 = 8. Then you subtract the 3 making the equation 3x = 5 and then you would divide the 3 making your answer 5/3.

Answer:

False

Step-by-step explanation:

It is False. 1 is the identity element for multiplication, because if you multiply any number by 1, the number doesn’t change. Identity elements are specific to each operation (addition, multiplication, etc.). So while 1 is the identity element for multiplication, it is NOT the identity element for addition.

Answer:

They both had the same amount of students watch the reality show.

Step-by-step explanation:

To find the number of students who watched the reality show in each teacher's class, just multiply the fraction by the total number of students per teacher.

For Mrs. Thorne's:

36 * (2/3) = 24 students

For Mrs. Lombardo's:

30 * (4/5) = 24 students

24 = 24 so they had an equal amount of students from each class watch the reality show.

Answer:

There is a area of triangle and there is two trapezium so 8×17=136

Answer:

1/5

Step-by-step explanation:

rise = 2 ft

run = 10 ft

slope = rise/run = 2/10 = 1/5

Answer: 1/5

Answer:

1/5

Step-by-step explanation:

The slope is the rise over the run

Y / x

2/10

1/5

Answer:

0, 1/18, and 1/36

Step-by-step explanation:

For i = 2, the probability it lands on 6 is 0, because you cannot sum to 2 with a 6. The same applies to i = 3 thru i = 6.

For the probability that at least one of a pair of fair dice lands on 6 for i = 7, there are only two possible ways, the first roll is a 6 and the second roll is a 7, and the first roll is a 1 and the second roll is a 6. The total amount of ways is 6 * 6 = 36, so the total probability is 1/18. This also applies to i = 8 thru i = 11.

For i = 12, there is only one way to get 12, the first dice lands on 6 and the second dice lands on 6. Assuming the dice are indistinguishable, the probability is 1/36.

The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.

We have,

The complementary probability of "at least one die lands on 6" is "neither of the dice lands on 6."

Therefore, you need to find the probability that neither of the dice lands on 6 for each possible sum i, and then subtract that probability from 1 to get the desired probability.

Let's go through the cases:

i = 2 (only possible sum with two dice):

In this case, both dice must show a 1.

The probability of this happening on a fair 6-sided die is

(1/6) * (1/6) = 1/36.

i = 3: The combinations are (1, 2) and (2, 1).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 4:

The combinations are (1, 3), (2, 2), and (3, 1).

The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.

i = 5:

The combinations are (1, 4), (2, 3), (3, 2), and (4, 1).

The probability of any of these happening is 4 * (1/6) * (1/6) = 1/9.

i = 6:

The combinations are (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).

The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.

i = 7:

The combinations are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).

The probability of any of these happening is 6 * (1/6) * (1/6) = 1/6.

i = 8:

The combinations are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2).

The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.

i = 9:

The combinations are (3, 6), (4, 5), and (5, 4).

The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.

i = 10:

The combinations are (4, 6) and (6, 4).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 11:

The combinations are (5, 6) and (6, 5).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 12:

The combination is (6, 6).

The probability of this happening is (1/6) * (1/6) = 1/36.

Now, sum up the probabilities for each case:

(1/36) + (1/18) + (1/12) + (1/9) + (5/36) + (1/6) + (5/36) + (1/12) + (1/18) + (1/18) + (1/36)

This simplifies to:

69/36 = 23/12

Thus,

The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.

Learn more about probability here:

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Answer:

A

Step-by-step explanation:

I know that 20 times 7 is 140 and if I take away 2 sevens that leaves 126. So 126 \div 7 = 18

Answer:

A. 18

Step-by-step explanation:

I took a photo of my work I didn't know how I could type that here

Tell me if I'm wrong :)

Answer:

y = - 3x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x + y - 1 = 0 ( subtract 3x - 1 from both sides )

y = - 3x + 1 ← in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes, thus

y = - 3x + c ← is the partial equation

To find c substitute (1, 4) into the partial equation

4 = - 3 + c ⇒ c = 4 + 3 = 7

y = - 3x + 7 ← equation of line in form y = mx + c

Answer:

draw a circle, and draw the degrees

Step-by-step explanation:

Answer:

I cant even see anything can you reupload your answer, please?

Step-by-step explanation:

Answer: 90,000

To find the LCM (Least Common Multiple) of a number, list the multiples of each number.

Multiples of 900

Since they're a lot, we will extend it to the short version.

900, 2700, 9900, 37800, 85500, 90000

Multiples of 30000

30000, 60000, 90000, 120000, 150000

Looking at both multiples, the least common multiple is 90000, as it is listed in both 900 and 30000.

Hence, 90,000 is the answer.

Answer:

True

Step-by-step explanation:

They can sustain themselves

Answer:

Natural freshwater ecosystems represent the terrestrial phases of the global hydrological cycle and include rivers, streams, lakes, ponds, wetlands, as well as groundwaters.

Answer:

[tex]{\huge{\green{\mathsf{z\:=\sqrt{\frac{4x}{3y}}}}}[/tex]

Step-by-step explanation:

Given the algebraic equation, [tex]{\huge{\green{\mathsf{x\:=\frac{3yz^2}{4}}}}[/tex], and that we must solve for z :

The first step is to multiply both sides by 4 to eliminate the fraction on the right-hand side of the equation:

[tex]{\huge{\green{\mathsf{x\:=\frac{3yz^2}{4}}}}[/tex]

[tex]{\huge{\green{\mathsf{(4)\:x\:=\frac{3yz^2}{4}(4)}}}[/tex]

4x = 3yz²

Next, divide both sides by 3y:

[tex]{\huge{\green{\mathsf{\frac{4x}{3y}\:=\frac{3yz^2}{3y}}}}[/tex]

[tex]{\huge{\green{\mathsf{\frac{4x}{3y}\:=z^2}}}[/tex]

Lastly, take the square root of both sides to isolate the variable, z :

[tex]{\huge{\green{\mathsf{\sqrt{\frac{4x}{3y}}\:=\sqrt{z^2}}}}[/tex]

[tex]{\huge{\green{\mathsf{z\:=\sqrt{\frac{4x}{3y}}}}}[/tex]

Therefore, the equation for z is:   [tex]{\huge{\green{\mathsf{z\:=\sqrt{\frac{4x}{3y}}}}}[/tex]

Please find attached photograph for your answer.

Hope it helps.

Do comment if you have any query.

He needed to make a total of 1980 + 630 = $2610

$2610 / 45 = 58

Answer: 58

Answer:

0.27

Step-by-step explanation:

0.1 8

x 0.50

-----------

000

900

x 1800

-----------

2700 = 0.27

13. 12008.

14. 59286.

15. 21459.

16. 80478.

17. 130567.

18. 11100.

19. Seventy-two thousand, one hundred eighty.

20. Eighty thousand, seven hundred eighty-six.

Hope This Helps...:)

Answer: a = 2.5 (an-1)

Step-by-step explanation: trust me;)

The function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is [tex]a_{n} = 8(2.5)^{n-1}[/tex].

sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is as a geometric sequence of  numbers.

[tex]a_{n} =ar^{n-1}[/tex]

Where,

[tex]a_{n}[/tex] is the nth term of the sequence or geometric progression

n is the total number of terms

r is the common ratio

and a is the first term

According to the given question

We have

A geometric progression

8, 20, 50, 125, 312.5

Now the common ratio for the above progression is given by

[tex]r = \frac{20}{8} = 2.5[/tex]

And the first term is

a = 8

Therefore, the function which is used to represent the above sequence is given by

[tex]a_{n} = 8(2.5)^{n-1}[/tex]

Hence, the function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is [tex]a_{n} = 8(2.5)^{n-1}[/tex].

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Answer:

A. 4/11

B. 2/11

Step-by-step explanation:

Use the given values to find the fractions (4+5+2=11)

Answer:

Hi! I hope this answer helps you.

In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x.

any vertical line in the plane can intersect the graph of a function at most once.

HOW TO DO THIS

take your pencil and place it on your paper vertically (up and down direction)

move the pencil across the paper to the right

if the pencil crosses more than two points on the line it is not a function

the first problem would be a function

the second problem would be a function

the third problem would not be a function

hope this helps !!!!

Answer:

24x^11

Step-by-step explanation:

4x^8*6x^3 can be rewritten as 24x^(3+8) - multiply 4 and 6

Now we just have 24x^11.

Answer:

The Coefficients in this expression are 10 and 3, while the constants are 5 and 1.

Step-by-step explanation:

Coefficients = The number that is in front of the variable.

Constant = Any number without a variable.

(Variables are the letters that you may find in an equation or function.)

Hope this helps you :)

Answer:

The coefficient are 10 and  3

The constants are 5 and 1

Step-by-step explanation:

A coefficient is the number in front of any known term.

A constant is a number by itself.

So the coefficient are 10 and  3

The constants are 5 and 1

Answer:

Step-by-step explanation:

Let the number is x.

2/3 of a number is 10:

0.15 times of the number is:

Correct choice is d

Answer:

Step-by-step explanation:

Number of uniforms can be bought:

Amount to be spent:

Remaining amount:

Answer:

Infinitely many solutions

Step-by-step explanation:

3x + 99 = 3 (x+33)

distribute 3 to x and 33

3 * x = 3x

3 * 33 = 99

3x + 99 = 3x + 99

If the expressions on both sides of the equal sign are the same, then solving for them would result in 0 = 0 meaning that the equation has infinitely many solutions

The circumference of a circle is the total length of the boundary of the circle. So that the length of lace trim required is 597.1429 cm.

The diameter of the table is 60 cm, which has 65 cm tablecloth hanging on its sides. The diameter of the cloth required would be the length from one side to the other side. So that the total diameter of the tablecloth is:

= 60 cm + 2*65 cm

= 60 cm + 130 cm

= 190 cm

The diameter of the tablecloth required is 190 cm.

Thus to determine the circumference of the tablecloth, we have;

C = 2[tex]\pi[/tex]r

   = [tex]\pi[/tex]D

where D is the diameter of the tablecloth.

C = [tex]\frac{22}{7}[/tex] x 190

   = 597.1429

C = 597.1429 cm

Therefore, the length of lace trim required for the edge of the tablecloth is 597.1429 cm.

Kindly check: https://brainly.com/question/13183446